FIT 1005 Networks & Data Communications
Lecture 2 – Data Transmission
Reference: Chapter 3
Data and Computer Communications
Eighth Edition
by William Stallings
Lecture slides by Lawrie Brown
Lecture slides also available at: http://users.monash.edu.au/~amkhan/fit1005/
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Data Transmission Terminology
• data transmission occurs between
a transmitter & receiver via some
medium
• guided medium
– e.g. twisted pair, coaxial cable, optical
fiber
• unguided / wireless medium
– e.g. air, water, vacuum
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Data Transmission Terminology-2
• direct link
– no intermediate devices
– Except amplifiers or repeaters
• point-to-point
– direct link
– only 2 devices share medium(link)
• multi-point
– more than two devices share the
medium (link)
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Data Transmission Terminology-3
• simplex
– one direction
> e.g. television
• half duplex
– either direction, but only one way at a time
> e.g. police radio
• full duplex
– both directions at the same time
> e.g. telephone
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Frequency, Spectrum and Bandwidth
• Time domain concepts: viewed as a function of time
– Can be analog or digital
– analog signal
> varies in a smooth way over time
– digital signal
> maintains a constant level then changes to another constant level
– periodic signal
> pattern repeated over time
– aperiodic signal
> pattern not repeated over time
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Analogue & Digital Signals
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Periodic Signals
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Sine Wave
• peak amplitude (A)
– maximum strength of signal
– measured in volts (V)
• frequency (f)
–
–
–
–
rate of change of signal
Hertz (Hz) or cycles per second
period (T) = time for one repetition
T = 1/f
• phase ()
– relative position in time
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Sine Wave - 2
• A sine wave can be represented as:
s(t) = A sin(2ft + )
t
where:
A – peak amplitude
f – frequency
t – time
 - phase angle
 - phase = Degrees
00
450
900
1350
1800
Radians
=0
= /4
= /2
= 3/4
=
00 = 
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Varying Sine Waves
s(t) = A sin(2ft + )
(a) A=1, f =1, ø = 00
(b) A=0.5, f =1, ø = 00
(c) A=1, f =2, ø = 00
(d) A=1, f =1, ø = Π/4 = 450
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Varying Sine Waves
s(t) = A sin(2ft + )
(a) A=1, f =1, ø = 00
(b) A=0.5, f =1, ø = 00
(c) A=1, f =2, ø = 00
(d) A=1, f =1, ø = Π/4 = 450
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Varying Sine Waves
s(t) = A sin(2ft + )
(a) A=1, f =1, ø = 00
(b) A=0.5, f =1, ø = 00
(c) A=1, f =2, ø = 00
(d) A=1, f =1, ø = Π/4 = 450
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Varying Sine Waves
s(t) = A sin(2ft + )
(a) A=1, f =1, ø = 00
(b) A=0.5, f =1, ø = 00
(c) A=1, f =2, ø = 00
(d) A=1, f =1, ø = Π/4 = 450
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Varying Sine Waves
s(t) = A sin(2ft + )
(a) A=1, f =1, ø = 00
(b) A=0.5, f =1, ø = 00
(c) A=1, f =2, ø = 00
(d) A=1, f =1, ø = Π/4 = 450
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Wavelength ()
• is distance occupied by one cycle
• between two points of corresponding phase in
two consecutive cycles
• assuming that the signal velocity is vs
then, we have:  = vsT
• or
 = vs / f (since T = 1/ f)
 and so, vs = f 
 especially when vs = c
c = 3*108 ms-1 (speed of light in free space)
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Frequency Domain Concepts
• signal are made up of many frequencies
• components are sine waves
• Fourier Analysis can shown that any
signal is made up of component sine
waves
• can plot frequency domain functions
Fourier Analysis:
The complex wave at the top can
be decomposed into the sum of
the three simple sine waves
shown here.
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Addition of Frequency
Components (T=1/f)
•
graph c is sum of graphs a & b
S(t) = A * sin [ (2) f t ]
•
(a) = 1*sin[ (2) f t ]
•
(b) = 1/3 * sin[ (2) (3f) t ]
•
(c) = (4/) * {
•
The scaling factor of (4/) is used to
produce the cumulative wave whose
maximum peak amplitude is close to 1.
1*sin[ (2) f t ]
+ 1/3 * sin[ (2) (3f) t ] }
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Frequency Domain
Representations
•
t
Frequency domain function of Fig 3.4c
S(f)
t
f
t
S(t)
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Frequency Domain Representations
•
Frequency domain function
of single square pulse
S(t)
S(f)
1
- X/2
+X/2
Fourier transform
t
S(t) = 1 for time period -X/2 to +X/2
= 0 elsewhere
Fourier transform
S(f) = 1 X sin( f X)
----------------fX
reference Page-839 William Stallings
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Frequency Domain Representations (Java Demo)
• Fourier series representation of any given
periodic signals
– Can be represented as a sum of sine and cosine
waveforms known as Fourier series.
– reference Page-836 William Stallings
• Fourier Series Applets in Java.
– http://www.falstad.com/fourier/index.html
– http://www.falstad.com/fourier/
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Spectrum & Bandwidth
• spectrum
– range of all frequencies contained in signal
• absolute bandwidth
– width of spectrum
• effective bandwidth
– often just bandwidth
– narrow band of frequencies containing most energy
• DC Component
– component of zero frequency
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Data Rate and Bandwidth
• any transmission system has a limited band of
frequencies
• this limits the data rate that can be carried
• square wave have infinite frequency
components and hence bandwidth
• but most of its energy in focused in first few
components (harmonics)
• limited bandwidth increases distortion
• have a direct relationship between data rate &
bandwidth
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Analog and Digital Data Transmission
• data
– entities that convey meaning
• signals & signalling
– electric or electromagnetic representations of data,
physically propagates along medium
• transmission
– communication of data by propagation and processing of
signals
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Complete frequency Spectrum
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Acoustic Spectrum (Analog)
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Audio Signals
•
•
•
•
freq range 20Hz-20kHz (speech 100Hz-7kHz)
easily converted into electromagnetic signals
varying volume converted to varying voltage
can limit frequency range for voice channel to
300-3400Hz
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Digital Data
• as generated by computers etc.
• has two dc components
• bandwidth depends on data rate
-5 volts
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Analog Signals
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Digital Signals
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Advantages & Disadvantages
of Digital Signals
•
•
•
•
cheaper than analog signalling
less susceptible to noise
but greater attenuation
digital now the preferred choice
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Transmission Impairments
• signal received may differ from signal transmitted
causing impairment:
– Analog transmission - degradation of signal quality
– digital transmission - bit errors
• most significant impairments are
1. attenuation and attenuation distortion
2. delay distortion
3. noise
Lets see these impairments one by one!
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Transmission Impairments: (1) Attenuation
•
•
•
•
where the signal strength falls off with distance
depends on transmission medium
It is a increasing function of frequency
received signal strength must be:
– strong enough to be detected
– sufficiently higher than noise so as to receive without error
• so we increase strength using amplifiers/repeaters
• so equalize attenuation across band of
frequencies we use
– e.g.. loading coils or amplifiers
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Transmission Impairments: (2) Delay Distortion
• only occurs in guided media
• propagation velocity varies with frequency
• hence various frequency components arrive at
different times
• particularly critical for digital data
– because some of the signal components of one bit
position will spill over into other bit positions, hence
– causing inter-symbol interference
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Transmission Impairments: (3) Noise
• noise is the additional signals that is inserted
between transmitter and receiver
• (1) thermal noise
–
–
–
–
–
–
due to thermal agitation of electrons
Present in all electronic devices & transmission media
Function of temperature
uniformly distributed
cannot be eliminated
Also referred as white noise
• (2) intermodulation noise
– signals that are the sum and difference of original
frequencies sharing a medium
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Transmission Impairments: (3) Noise
• crosstalk
– a signal from one line is picked up by another
• impulse
– irregular pulses or spikes
> eg. external electromagnetic interference
–
–
–
–
short duration
high amplitude
a minor annoyance for analog signals
but a major source of error in digital data
> a noise spike could corrupt many bits
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Channel Capacity
• Channel capacity (C) is the maximum rate at which
data can be transmitted over a given
communication channel.
• We need to consider:
1. Data rate, measured in bits per second (bps), is the rate at
which data can be communicated.
2. The Bandwidth (B) of channel, measured in cycles per
second or Hertz.
3. Noise, the average level across the communication channel.
4. Bit Error Rate on the channel resulting from the noise.
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Channel Capacity and bandwidth
• Communication facilities are expensive
• Greater the bandwidth, more expense
• Bandwidth limitations are due to physical
properties of transmission mediums
• want to make most efficient use of channel
capacity
• Other main constrain being noise
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Nyquist Bandwidth
• Nyquist formula (for noise free channels):
Channel capacity, C = 2B
( two voltage level only)
• if rate of signal transmission is 2B then it can carry
signal with frequencies no greater than B Hz
– i.e. given bandwidth B, highest signal rate is 2B bps
• for binary(2) signals, a transmission rate of C=2B
bps needs a bandwidth of B Hz
• With multilevel signaling, the Nyquist formulation
becomes: C = 2B log2 M,
(where M is the number of discrete signal or voltage levels.)
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Nyquist Bandwidth: Example
• In a noise free channel, the channel capacity, in
bps, of the channel is at best twice the
bandwidth of the channel. C=2B
• As an example, consider a telephone line (voice
channel) used to transmit digital data:
– On a telephone channel with a frequency range from
300Hz to 3400Hz,
– The bandwidth is
B = f highest – f lowest
B = 3400 – 300 = 3100Hz
– Hence, the channel capacity is at best: C=2B
C = 2 x 3100 = 6200 bps
– This assumes two level (binary) signalling.
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Nyquist Bandwidth -2
• In binary signalling, two voltage levels are used
• The signal rate can be increased by using more
than two signal levels (multilevels)
• With multi-level signalling
• Nyquist Formula is: C = 2B log2M
where M is the number of voltage levels used
• Increase the data rate by increasing signal
voltage levels (multiple voltage levels)
– at a cost of receiver complexity
– Limitations are added by noise & other impairments
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Shannon Capacity Formula
• consider relation of data rate, noise & error rate
– faster data rate shortens each bit, so bursts of noise affect more bits
– given noise level, higher rates means more errors
• Shannon developed formula relating these to signal-to-noise
(SNR) ratio
Capacity C = B log2(1+ SNR)
– This is the theoretical maximum capacity
– but we can only get lower capacity in practise
– because formula only assumes white noise (thermal noise)
• Signal to noise ratio is usually expressed in decibels dB
SNRdB = 10 log10 (SNR)
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Logarithms formulas / rules
A = Log b N
N = bA
Logb x
b
=x
Logb (A B) = Logb(A) + Logb(B)
Logb (A /B) = Logb(A) - Logb(B)
Logb 1 = 0 for any base b
Logb b = 1 for any base b
Logb (A ) = Logn(A)
Logn(b)
Logb (An) = n Logb(A)
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Shannon Capacity Formula: Example
1. The spectrum(BW) of a channel
is between 3 MHz to 4 MHz and
SNRdB = 24 dB.
Bandwidth (B)= (4 – 3) = 1 MHz
24 dB = 10 log10 (SNR)
SNR = 102.4
SNR = 251
2. What is the capacity of the
channel?
Using Shannon’s formula,
3. How many signalling
levels are required to
achieve this capacity of
8 Mbps?
Using Nyquist formula:
C = 2B log2M
8 106 = 2 x 106 x log2M
4 = log2M
M = 24
M = 16
C = 106 x log2(1+ 251)
≈ 106 x 8 = 8 Mbps
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Decibels and Signal Strength
Amplifiers and Repeaters:
• Signal strength: important parameter in
communication systems
• Loss or attenuation of signal strength
• Amplifiers: regain signal strength (used in analog
systems)
• Repeaters: regenerate signals used in digital
networks
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Decibels and Signal Strength- 2
Decibel (dB)
• Signal strength: gain or loss is expressed in dB
• Decibel is a ratio of two signal levels, say output and input
of a communication system
• The ratio could be Power i/p to Power o/p
• Or the ratio of signal power to noise power
• Or signal voltage to noise voltage
• Or signal i/p voltage to o/p voltage
• As long as it the ratio measured in a special way called
decibels and expressed as dB
• These ratios can be +ve or –ve also known as Gain or Loss
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Decibels and Signal Strength- 3
Gain or Loss in dB
• Signal Power Gain (or simply Gain) in dB is:
GdB = 10 log10 Pout / Pin
where
Pin = input power level
Pout = output power level
log10 = logarithm to the base 10
• Loss in dB is:
LdB
= - 10 log10 (Pout / Pin )
or
= 10 log10 (Pin / Pout )
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Decibels and Signal Strength- 4
Example: If a signal with power level of 10 mW is inserted at the
input of a communication system and a power of 5 mW is
extracted at the output, calculate the loss in dB.
Pout = 5 mW
Pin =10 mW
LdB = 10 log10 Pin / Pout
= 10 log10 (10 mW) / (5 mW)
= 10 log10 (2)
= 10 log10 2 = 10 x 0.3
= 3 dB.
OR
LdB = -10 log10 Pout / Pin
= -10 log10 (5 mW) / (10 mW)
= -10 log10 (0.5)
= -10 log10 0.5 = 10 x - 0.3
= 3 dB.
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Decibels and Signal Strength- 5
Decibel can also be used as a ratio of input
voltage to output voltage in a communication
system:
LdB
= 10 log10 Pin / Pout
= 10 log10 [(V2in )/R]
/ [(V2out )/R]
= 2 x 10 log10 Vin / Vout
= 20 x log10 Vin / Vout
where P = V2 / R
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Decibels and Signal Strength- 6
• The decibel-Watt (dBW) is another common
measure used in microwave systems:
(which is referenced to 1W)
PowerdBW = 10 log (PowerW / 1 W)
• Decibel-milliWatt and decibel-millivolt are also
defined: (which is referenced to 1mW or 1mV)
PowerdBm
= 10 log (PowermW / 1 mW)
VoltagedBmV = 20 log (VoltagemV / 1 mV)
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Summary
•
•
•
•
•
looked at data transmission issues
frequency, spectrum & bandwidth
analog vs digital signals
transmission impairments
decibels and signal strengths
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